The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  0  1  1 2X  1  0  1 2X+2  1  1  X  1
 0  X  0 X+2 2X 3X+2  0  X 2X+2 X+2  2 3X  X  2  2  X X+2  X  X  X 3X+2 2X X+2 X+2
 0  0  2  0 2X  2  2 2X+2 2X+2 2X+2 2X 2X+2 2X  0 2X+2  2  0  2 2X  0  0 2X+2  0 2X+2
 0  0  0  2  2 2X+2  2 2X  0  0  2  2 2X 2X 2X+2 2X 2X 2X+2 2X+2  2  0 2X 2X+2 2X

generates a code of length 24 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+30x^20+146x^21+184x^22+498x^23+351x^24+500x^25+174x^26+124x^27+16x^28+10x^29+5x^30+2x^31+2x^32+4x^34+1x^38

The gray image is a code over GF(2) with n=192, k=11 and d=80.
This code was found by Heurico 1.16 in 0.031 seconds.